Open Access

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Advances in Difference Equations20072007:067492

DOI: 10.1155/2007/67492

Received: 26 November 2006

Accepted: 23 February 2007

Published: 11 April 2007

Abstract

We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology
(2)
Department of Mathematics and Computing, University of Veszprém

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Copyright

© R. P. Agarwal and M. Pituk. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.